"simple" math question

**ceroseven** · February 4th 2010, 06:38 AM

If cosA=cos B, then when does A=B? (Always, sometimes, never, infinite etc).

**felper** · February 4th 2010, 06:51 AM

No. Counterexample:

$\cos(0)=\cos(2\pi)=1 \Rightarrow 0 \neq 2\pi$

If you work on the interval $\left[ 0, \pi \right]$ , then $\cos(a)=\cos(b)\Rightarrow a=b$

**ceroseven** · February 4th 2010, 11:17 AM

So what is the answer.. Never or sometimes?

**bigwave** · February 4th 2010, 12:09 PM

it is always the same when it is a sign identity

$\cos\left({\theta}\right) = \cos\left({-\theta}\right)$

since $\beta$ would just be a reflection of $\alpha$ off the x axis then

$\cos{\alpha} = \cos{\beta}$

example:

$\cos\left({\frac{\pi}{4}}\right)<br /> =\cos\left({-\frac{\pi}{4}}\right)<br /> = \frac{\sqrt{2}}{2}$

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